1. Field of the Invention
This invention relates generally to communication systems wherein modulated carrier signals convey data in digital form and more particularly to the implementation of coherent demodulators and signal phase estimators for such systems that must accommodate undesired signal-phase values and temporal variations thereof.
2. Description of the Related Art
In many carrier-based communication systems the transmit signals used to convey information are of the form
stx(ttx)=Atx(ttx)xc2x7sin[xcfx89c txxc2x7ttx+xcfx86m tx(ttx)]xe2x80x83xe2x80x83(1)
where ttx represents (relative) transmit time, xcfx89c tx represents the transmit radian carrier frequency in radians per second, xcfx86m tx(ttx)) represents signal phase variations attributable to any phase modulation effected and Atx(ttx) represents the signal""s amplitude. When the information transmitted is digital in form, the time continuum is generally divided into a succession of contiguous signaling (modulation) intervals and, for each signaling interval, log 2 m (uncoded or coded) data bits select one of m pre-specified options for varying the signal""s phase and/or amplitude during the signaling interval. For this invention, the signal""s phase may be varied (modulated) to convey digital data using any one of many different modulation methods including m-ary phase shift keying (PSK), m-ary continuous-phase frequency shift keying (CPFSK) and m-ary CPFSK with modulation and convolutional data encoding effected jointly. The signal""s amplitude may vary with time as a consequence of implementing an amplitude modulation method such as m-ary amplitude shift keying (ASK) or incidentally, e.g., due to signal filtering effected. For m-ary ASK, modulation phase component xcfx86m tx(ttx) has a constant value considered herein to be zero radian. This invention also applies to several modulation methods for which signal amplitude and signal phase are varied jointly to convey digital data as for m-ary quadrature amplitude modulation (QAM).
For each of several modulation methods, the transmitted signal can be modeled equivalently as either a phase modulated signal or an amplitude-modulated signal where the signal amplitude is either a real or complex-valued function of time. Such methods are considered to be phase modulation methods herein irrespective of the means used to generate the signals transmitted. Further, for communication systems wherein digital data are transmitted via signaling bursts rather than continuouslyxe2x80x94as in time division multiple access (TDMA) systemsxe2x80x94a transmit signal is modeled by assigning a value of zero to the signal""s amplitude whenever signal transmission is disabled.
A transmit signal propagates from its point of origin to one or more receiver locations via one or more communication channels comprised of wire-line, wireless or electronic relay means, or any combination thereof. For a transmit signal representable by Equation 1, a signal received at a receiver location is of the form
srx(t)=s(t)+nxcexa3(t)xe2x80x83xe2x80x83(2)
where t represents (relative) receive time, s(t) is a delayed, attenuated and generally-distorted version of the transmit signal,
s(t)=A(t)xc2x7sin[xcfx89cxc2x7t+xcfx86m(t)+xcfx86u(t)],xe2x80x83xe2x80x83(3)
and nxcexa3(t) represents a sum of noise and undesired signals which exacerbate generation of an exact (delayed) replica of the transmit data at the receiver. In accord with common practice, radian carrier frequency xcfx89c is assumed to be perfectly known at the receiver; frequency uncertainties that result from imperfect frequency synthesis within transmit, relay and receive subsystems and any doppler shift experienced by the signal in propagating to the receiver are considered to affect the value of signal phase xcfx86u(t): a phase variation that is unintended and undesired. Signal parameter xcfx89m(t) represents the modulation component of the received signal""s phase when phase modulation is effected; otherwise, its value is considered herein to equal zero radian.
For a communication system wherein undesired signal-phase xcfx86u(t) can be made to vary slowly relative to and be distinguishable from phase xcfx86m(t), the most effective use of signal power can generally be achieved by employing a coherent demodulator to process the received signal. Ideally, a portion of the receiver would generate an exact replica of signal phase xcfx86u(t) and subtract this replica from the phase of the received signal to form a signal that exhibits no undesired phase variations; the latter signal would then be demodulated coherently to generate a nominal replica of the transmitted data stream. For many classes of modulation methods, prior art provides means for coherently demodulating signals which exhibit no undesired phase variations that can be implemented effectively whenever time intervals spanned by received modulation symbols, modulation intervals, can be accurately determined at the receiver""s location.
In practice, undesired signal-phase xcfx86u(t) cannot be replicated exactly at a receiver location, but an estimate of xcfx86u(t) can often be generated with sufficient accuracy to allow the implementation of nearly-ideal coherent demodulationxe2x80x94particularly when m-ary PSK is used to generate signal modulation phase xcfx86m(t). For ideal (unfiltered) m-ary PSK, the signal""s amplitude has a constant value and xcfx86m(t) assumes any one of m phases that are equally spaced in a 2xcfx80 radians phase range during each modulation interval. As is well known, an mth-order nonlinear device having a received m-ary PSK signal applied to its input port and a bandpass filter that rejects undesired components in the nonlinear device""s output signal can generate a signal having a radian center frequency of mxc2x7xcfx89c and phase mxc2x7xcfx86u(t) accompanied by a noise signal that derives from the nxcexa3(t) component of the received signal. That is, an mth-order nonlinear device provides a means for distinguishing mxc2x7xcfx86u(t) from xcfx86m(t) when m-ary PSK is implemented. The nonlinear device""s output signal is typically filtered by a relatively narrow-band phase-lock loop to generate a sufficiently accurate estimate of phase mxc2x7xcfx86u(t) notwithstanding the presence of noise in the received signal. An ambiguous estimate of phase xcfx86u(t) can be determined there from by effectively dividing mxc2x7xcfx86u(t) by m. An m-fold ambiguity that derives from the divide operation is generally accommodated by either 1) differentially encoding the transmit data stream and differentially decoding the demodulated data stream in a manner appropriated for the value of m implemented or 2) periodically embedding a priori specified symbols within the transmit date stream which replicate properly in the demodulator only when the appropriate one of m ambiguous phase values is selected. Alternatively, phase-lock loops that incorporate other forms of nonlinearities to distinguish xcfx86u(t) from xcfx86m(t), e.g., a Costas loop, can be used to provide the desired phase estimate when m-ary PSK modulation is employed.
Phase-lock loops that incorporate nonlinearities as described in the preceding paragraph have attributes that limit system performancesxe2x80x94particularly when burst signals are used to convey data as in TDMA systems. As is well known, the time required for a phase-lock loop to achieve lock is statistically distributed and occasionally exceeds the mean acquisition time by a considerable amount (such an event is referred to as a phase-lock loop hang-up), and the noise component of the received signal occasionally causes a locked loop to cycle slip, i.e., to lose and regain lock in a manner whereby the accumulated phase of the loop""s output signal differs from the accumulated phase of the (multiplied) signal being tracked by one or more cycles. Further, as the nonlinearity orderxe2x80x94the value of mxe2x80x94is increased, the power spectral density of the noise signal at the output of the nonlinearity increases relative to the level of the desired output signal because a larger number of signal by noise products are generated. Correspondingly, the bandwidth of the signal phase tracking loop must be made increasingly narrow relative to the modulation symbol transmission rate to achieve acceptable steady-state performance. Filtering an m-ary PSK transmit signal to reduce spectral sidelobe levels can also cause tracking-loop performance to degrade.
For a TDMA system wherein estimates of carrier frequency, carrier phase and modulation interval timing are generated at the beginning of each received signal burst by processing preamble symbols (before data demodulation is initiated), making the bandwidths of tracking loops sufficiently small to achieve acceptable steady-state performance can necessitate the use of an unacceptably long burst preamble. For a symbol-synchronous TDMA system, i.e., for a TDMA system wherein signal modulation symbol time bases and carrier frequencies are maintained in accurate synchronism with the time base and frequency, respectively, of a (pulsed-envelope) network timing signal, the transmission of burst preambles can be avoided by converting the received signal bursts into digitally represented sample sequences that are stored in digital memory and implementing xe2x80x9cmultiple-passxe2x80x9d digital processing. Typically, in-phase and quadrature components of the received signal are integrated over each modulation interval and converted into digital form or, equivalently, appropriate digitized signal sample values are summed to generate the sample sequences processed. Paired in-phase and quadrature sample values are interpreted as vectors from which vectors that have phase angles equal to m times the sample vector angles are generated and processed digitally over a sliding processing window to form estimated values of mxc2x7xcfx86u(t) modulo 2xcfx80 radians. These values are divided by m to generate estimated values of xcfx86u(t) that exhibit an m-fold ambiguity. In turn, stored (delayed) sample vectors are rotated in phase as appropriate to correct for the estimated undesired signal-phase values and the phase-corrected sample vectors are demodulated to generate a received data sequence. Of course, such multiple-pass digital processing does not circumvent the fundamental limitations of mth-order nonlinear phase estimation methods.
Estimation of an undesired signal-phase component can similarly be accomplished when certain combinations of phase and amplitude modulations are used to convey data, e.g., as for selected forms of QAM. However, important modulation methods are incompatible with the use of nonlinear processing to distinguish undesired signal-phase variation xcfx86u(t) from signal phase modulation xcfx86m(t)xe2x80x94including most forms of m-ary CPFSK. Circumvention of mth-order nonlinear processor performance limitations is also of interest.
One alternative approach to distinguishing xcfx86u(t) from xcfx86m(t) relies on estimation of xcfx86m(t) and, effectively, subtraction of the estimated modulation phase from the phase of the received signal to generate a signal that, ideally, would exhibit phase variations xcfx86u(t) only. Estimators that incorporate this alternative approach are often referred to as either decision-directed estimators or data-aided estimators. Their utility derives from the premise that sufficiently accurate estimation of xcfx86u(t) can be accomplished using an estimate of xcfx86m(t) that is not sufficiently accurate for demodulation purposesxe2x80x94at least whenever the error in the locally generated estimate of xcfx86u(t) is large. Proper operation of a decision-directed estimator requires that the modulation means and estimator be implemented jointly in a manner whereby errors made in estimating xcfx86m(t) only temporarily affect estimator operation and contribute only incrementally to errors made in estimating xcfx86u(t) and demodulating the received signal. This requirement substantially limits the scope of applications for which decision-directed (and data-aided) estimators can be implemented effectively.
Therefore, one object of the present invention is to provide means for coherently demodulating a received digitally-modulated carrier signal that accommodates an undesired signal-phase component and temporal variations thereof rather than requiring separate estimation of said undesired signal-phase component.
Another object of the invention is to provide means for generating a sequence of estimated values of an undesired signal-phase component for a received digitally-modulated carrier signal.
Another object of the invention is to provide means for coherently demodulating a received digitally-modulated carrier signal comprised of a succession of signal bursts that accommodates an undesired signal-phase component and temporal variations thereof and requires, at most, a few preamble and postamble symbols to be transmitted at the beginning and end of each signal burst, respectively.
Another object of the invention is to provide means for generating a sequence of estimated values of an undesired signal-phase component for a received digitally-modulated carrier signal comprised of a succession of signal bursts of the aforesaid type during the on-time of each signal burst received.
Another object of the invention is to provide means for coherently demodulating multiple received digitally-modulated carrier signals that are each comprised of a succession of non-overlapping signal bursts of the aforesaid type as in TDMA systems.
Another object of the invention is to provide means for generating sequences of estimated values of undesired signal-phase components for multiple received digitally-modulated carrier signals that are each comprised of a succession of non-overlapping signal bursts of the aforesaid type during the on-time of each signal burst received.
These and other objects of the invention are provided by a Composite-Trellis Processor (CTP) system and method which processes a received digitally-modulated carrier signal that has an undesired phase component as appropriate to effect nearly-ideal coherent demodulation and/or generate a sequence of estimated values of said undesired signal-phase component. Demodulation and forward error correction (FEC) decoding are effected jointly for some modulation methods, e.g., for convolutionally encoded m-ary CPFSK.
For applications in which accurate estimates of the undesired signal-phase and modulation interval timing can be provided, a Maximum Likelihood Sequence Estimator (MLSE) can be implemented using prior art which reconstructs the transmitted data sequence with a minimal number of erroneous decisions that result from additive receiver noise (when the noise is white and Gaussian distributed). Such an estimator correlates the received noisy signal with hypothesized signals generated locally for all possible ways that a trellis diagram can be traversed over successive modulation intervals (as a consequence of different sequences of data symbols being transmitted) and determines the optimum path through the trellis diagram, i.e., the path for which the correlation value is largest. Given said optimum path, the sequence of symbols most likely to have been transmitted can easily be determined there from.
The Viterbi maximum likelihood processing algorithm provides a means for implementing a MLSE in an iterative manner, that is, by executing one processing cycle following each modulation interval (or following each of a specified number of contiguous modulation intervals for some applications). The processing operations performed principally generate values for what are often referred to as path metrics (or state metrics) and path histories, one each per to state in a trellis diagram. Each path metric is a cumulative measure of the correlation between the received signal and a locally-generated hypothesized signal that traverses the trellis diagram along a surviving path that terminates at its associated to state. A path history for a surviving path can be represented by a sequence of states traversed by the path, the sequence of modulation symbols that would cause said path to be traversed or both sequences, depending on the specific application. The sequence of modulation symbols for a path can oftenxe2x80x94but not always, as shown belowxe2x80x94be determined from the sequence of states traversed by the path.
A CTP is nominally a MLSE for which the applicable trellis diagram is formed in accord with the teachings of this invention; thus, prior art for implementing MLSEs or relevant variants, augmentations, derivatives or counterparts thereof can be used to implement a CTP. Herein, exemplary embodiments of this invention are described for the case where the Viterbi algorithm and refinements thereof are used to implement CTPs. The embodiment descriptions presented provide an adequate basis for those skilled in the art to implement CTPs using other MLSE implementation means, and such alternative implementations are encompassed by this invention.
For a signal processed in accordance with a CTP system and method, allowed values of signal parameters at a succession of time instants that change as a consequence of the modulation effected are describable abstractly by a trellis diagram designated herein as a root trellis diagram. A root trellis diagram generally consists of equal integer numbers of from states and to states and information descriptive of allowed transitions between from states and to states for each of a succession of modulation intervals in accord with prior art. Depending on the modulation and data encoding means implemented, a state in a root trellis diagram can correspond to a value for a single signal parameter at an instant in time, or a combination of values which collectively characterize multiple signal parameters and the contents of any memory elements that affect from state to to state transitions, e.g., the contents of a data register within a convolutional encoder, at an instant in time. For brevity, that portion of a state""s representation which corresponds to a value for the signal""s phase is referred to herein as a phase state, with the understanding that a state is often represented completely as a concatenation of a phase state and one or more other partial state representations, e.g., a code state, an amplitude state and so forth. The time instant at which parameter values applicable to a state are valid is often taken to be either just before or just after the beginning of a modulation interval. A transition between from state and to state parameter values can occur near instantaneously, as for modulation phase values when unfiltered m-ary phase shift keying (PSK) is implemented, or throughout the time interval between the time instants at which from state and to state parameter values are valid, e.g., throughout a modulation interval as for m-ary CPFSK signals. This invention applies whenever the parameter value(s) associated with a state in a root trellis diagram explicitly or implicitly includes a value for the modulation phase of the transmitted signal, including a constant modulation phase value, e.g., zero radian, for m-ary ASK, and the phase of the received signal processed includes undesired component xcfx86u(t). The number of phase states for a root trellis diagram ranges from one for m-ary ASK to sixty-four or more for m-ary CPFSK when the denominator of the signal""s modulation index expressed as an irreducible ratio of integers has a large value.
The allowed transitions between states in a root trellis diagram are determined by the modulation means and, when used, data encoding means implemented. For many designs, each from state may transition to either of p predetermined to states, each to state may be transitioned into from either of p predetermined from states, and each demodulator decision represents log 2p bits of received digital data. For each transition in a root trellis diagram, the manner in which each applicable signal parameter varies with time during the modulation interval and a value for the correct demodulator decision are pre-specified (known a priori within a CTP).
A CTP performs processing operations in accord with a composite trellis diagram formed by combining progressively phase-displaced versions of a root trellis diagram and, for some embodiments of this invention, phase migration transitions. Each phase-displaced root trellis diagram in a composite trellis diagram is designated herein as a component trellis diagram, and the phase offset (displacement) for a component trellis diagram can equal any value. When the phase offset for a component trellis diagram equals zero radian, the component trellis diagram is identical to its associated root trellis diagram. The number of phase states in a composite trellis diagram generally equals the number of phase states in its associated root trellis diagram multiplied by the number of component trellis diagrams in the composite trellis diagram. Typically, the signal phase values associated with the phase states in a composite trellis diagram are equally spaced and the signal phase continuum is, thus, uniformly quantized with the phase quantization step size being equal to the phase range spanned by the signal phase values divided by the number of phase states in the composite trellis diagram. Such phase quantization causes a CTP""s performance to degrade with respect to the performance of an ideally implemented coherent processor, but the performance degradation can generally be made small by making the number of phase states sufficiently large, i.e., by making the number of component trellis diagrams in the composite trellis diagram sufficiently large. However, the complexity of a CTP is nominally proportional to the number of component trellis diagrams in the composite trellis diagram and said number is normally specified to provide an acceptable compromise between loss in performance due to phase quantization error and implementation complexity.
For some embodiments of this invention, the root trellis diagram has attributes that allow a composite trellis diagram to be comprised of only the root trellis diagram (or, for implementation convenience, a phase-shifted version thereof) and, when applicable, phase migration transitions. That is, the number of component trellis diagrams in a composite trellis diagram can be equal to one. For example, when the modulation method implemented is m-ary CPFSK, the number of phase states in the root trellis diagram can be sufficiently large for the phase quantization step size to be acceptably small without resort to combining two or more component trellis diagrams to achieve that end.
A composite trellis diagram that does not include phase migration transitions can accommodate undesired signal-phase xcfx86u(t) to within a phase quantization error when xcfx86u(t) equals, or varies only moderately relative to, an arbitrary constant value, e.g. as for signal bursts in TDMA systems that have short durations. Phase migration transitions are typically incorporated into a composite trellis diagram to accommodate both decreases and increases in the value of xcfx86u(t) for all distinguishable values thereof. That is, each phase migration transition typically allows a transition in the composite trellis diagram to occur for which the change in signal phase is either smaller or larger than the phase change for an associated transition in a component trellis diagram. Also, phase migration transitions are typically specified to recur periodically over time intervals which each span a specified number of modulation intervals, a phase migration period, and allow migration between phase states in the composite trellis diagrams to occur gracefully over extended intervals of time.
Fortuitously, considerable latitude exists in specifying allowed phase migration transitions. Typically, they are specified so that each to state for a phase migration transition is xe2x80x9cphase-adjacentxe2x80x9d to a to state for an associated transition in a component trellis diagram so that phase quantization error is minimized. The phase state in the composite trellis diagram for which the signal phase value is largest is considered to be adjacent to the phase state for which the signal phase value is smallest, and phase migration transitions that accommodate signal phase changes between said largest and smallest phase state values are required to accommodate large-scale variations in xcfx86u(t). For a given number of phase states in a composite trellis diagram, the maximum rate of change in xcfx86u(t) accommodated is greatest when the phase migration period spans only one modulation interval. However, to achieve nearly-ideal bit error probability (BEP) and/or signal phase estimation performances, the phase migration period generally must span sixteen to sixty-four or more modulation intervals depending on the modulation method implemented. Normally, the phase migration period is specified to provide an acceptable compromise between BEP and/or signal phase estimation performances and the rate of change in xcfx86u(t) that can be accommodated. Additionally, the phase migration transitions and phase migration period generally must be specified so that the phase migration transitions do not cause Hamming or squared Euclidean distances, whichever applies, for the composite trellis diagram to become unacceptably smaller than corresponding distances for the root trellis diagram.
This invention provides for implementing a CTP either in rigorous accord with a specified composite trellis diagram and associated modulation method or in an expedient manner that provides a preferred tradeoff between processor performance and implementation complexity for many applications. Such alternative methods for processing the received signal are categorized as rigorous processing methods and expedient processing methods, respectively. For either type of processing method, path history values within a CTP implemented using the Viterbi algorithm can be generated either directly or indirectly with the preferred embodiment for a given application being principally determined by implementation complexityxe2x80x94not by processor performance.
For direct path history generation, each path history value represents the sequence of states and/or the sequence of modulation symbols for the surviving path that terminates in the to state for which the path history value is generated. Each demodulator output symbol generated is derived from the xe2x80x9coldestxe2x80x9d information stored in a path history value. Often, the number of successive modulation symbols for which path sequence information is stored is referred to as the trellis traceback (or chainback) depth. Its value is specified to be sufficiently large to achieve an acceptable tradeoff between BEP performance and implementation complexity for the signal modulation and FEC coding methods employed.
For indirect path history generation, a xe2x80x9cpath historyxe2x80x9d value for a to state often designates either completely or partially the value of the from state for the winning from state to to state transition rather than a sequence of symbols or trellis states. For such indirect path history generation, the actual path history for a to state is determined through the implementation of well known prior-art traceback (chainback) means. Trellis traceback is not required when path histories are generated directly.
For both rigorous processing methods and expedient processing methods, the Viterbi algorithm is implemented identically for to states not allowed to be transitioned into via phase migration transitions during a processing cycle. Herein, to states of said type are designated as no-migration to-states. The most likely of all allowed transitions into each no-migration to-state is determined and corresponding path metric and path history values are updated accordingly for each iteration of the Viterbi algorithm.
For migrate-to to-states, i.e., for to states that may be transitioned into via phase migration transitions for a processing cycle, the processing operations performed to update path metric values depend on whether a rigorous processing method or an expedient processing method is implemented. When the Viterbi algorithm is implemented rigorously, each path metric value for a migrate-to to-state is updated by 1) calculating a candidate path metric value for each allowed transition into the migrate-to to-state, including phase migration transitions, 2) comparing all candidate path metric values for the migrate-to to-state to determine the best path metric value thereof and 3) setting the path metric value for the migrate-to to-state equal to the best path metric value so determined. Path history values for migrate-to to-states are updated in accord with winning trellis transitions, i.e., trellis transitions for which path metric values are best, including winning phase migration transitions, using either direct or indirect path history generation methods as described above.
For a rigorous processing method, the presence of phase migration transitions substantially increases processor complexity since both matched-filter values and branch-metric values appropriate for the phase migration transitions are generated in addition to generating and comparing additional candidate path metric values. The added complexity that derives from the presence of phase migration transitions can be reduced markedly without significantly degrading processor performance for most applications by implementing an expedient processing method. For an expedient processing method, each phase migration transition is specified to connect a migrate-from to-state to a migrate-to to-state and updated path metric and path history values for migrate-to to-states are selected from appropriate provisional path metric and path history values, respectively, calculated as described above for no-migration to states, i.e., as if no phase migration transitions were allowed.
Typically, for an expedient processing method, each phase migration transition connects a migrate-to to-state to a phase-adjacent migrate-from to-state to minimize performance degradation attributable to phase quantization. The phase value for a migrate-from to-state may be either smaller or larger than the phase value for a migrate-to to-state connected thereto. Furthermore, multiple phase migration transitions can concurrently terminate at a migrate-to to-state, e.g. phase migration transitions may concurrently connect both to states that are phase adjacent to a to state to the to state. As for rigorous processing methods, the aggregate of phase migration transitions in a composite trellis diagram generally must accommodate both incremental increases and incremental decreases in the undesired signal-phase value for arbitrary values thereof.
For an expedient processing method and each migrate-to to-state, the path metric value for the migrate-to to-state is updated by first generating provisional path metric values for the migrate-to to-state and all migrate-from to-states connected thereto by phase migration transitions as appropriate for no-migration to-states, i.e., as if there were no phase migration transitions. Then, the path metric value for the migrate-to to-state is updated by setting it equal to the best provisional path metric value so determined. Attendantly, provisional path history values for the applicable to-states are generated and the path history value for the migrate-to to-state is updated by setting it equal to the provisional path history value that corresponds to the best provisional path metric value.
Output signals generated by a CTP include a demodulated data symbol stream and/or successive estimated values of the undesired signal-phase component. Since a distinct hypothesized value of xcfx86u(t) is associated with each component trellis diagram, ambiguous estimates of xcfx86u(t) can be derived from either directly generated or xe2x80x9ctracebackedxe2x80x9d path history values that represent successive winning component trellis diagrams. The phase ambiguity is often xe2x80x9cnp-foldxe2x80x9d where np equals the number of phase states in a component trellis diagram. An appropriate traceback depth is mechanized for each output signal generated. That is, the traceback depths applicable to data demodulation and undesired signal-phase estimation can have different valuesxe2x80x94including zero for signal phase estimation. Note also that the traceback depth(s) required to provide near-ideal CTP performance is (are) minimized by deriving output decisions from successive path histories for to states that have the best overall path metric. Deriving output signals from successive path history values for a pre-specified state can result in unacceptable performance since merge distances for a composite trellis diagram can be substantially larger than merge distances for its associated root trellis diagram.
This invention also provides effective means for implementing CTPs which each demodulate and/or estimate the undesired phase of a signal burst or a succession of signal bursts which may originate at one or more transmit terminals, e.g., as in a TDMA system. Specifically, means for initializing and xe2x80x9ctailing-offxe2x80x9d operation of a CTP that provide for effective processing of burst signals are provided by this invention.
The features and advantages described in the specification are not all-inclusive, and particularly, many additional features and advantages will be apparent to one of ordinary skill in the art in view of the drawings, specification, and claims hereof. Moreover, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter, resort to the claims being necessary to determine such inventive subject matter.